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A003140 Number of coprime chains with largest member prime(n).
(Formerly M0896)
2

%I M0896

%S 1,1,2,3,9,10,19,20,32,84,85,161,212,214,260,521,818,820,1189,1406,

%T 1415,2005,2375,3351,5698,6122,6141,6600,6623,7270,23993,26735,33686,

%U 33753,55735,55750,66498,85117,90310,147374,165450,165479,249822,250176

%N Number of coprime chains with largest member prime(n).

%C A coprime chain is a nonempty set of integers greater than 1 such that all primes <= the largest member divide exactly one term of the set. - _Charles R Greathouse IV_, Apr 24 2013

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Charlie Neder, <a href="/A003140/b003140.txt">Table of n, a(n) for n = 1..62</a>

%H R. C. Entringer, <a href="https://doi.org/10.1090/S0002-9939-1965-0184914-5">The number of coprime chains with largest member n</a>, Proc. Amer. Math. Soc., 16 (1965), 806-810.

%H R. C. Entringer, <a href="/A003139/a003139.pdf">The number of coprime chains with largest member n</a>, Proc. Amer. Math. Soc., 16 (1965), 806-810. [Annotated scanned copy]

%H R. C. Entringer, <a href="https://doi.org/10.1090/S0002-9939-1965-0177974-9">Some properties of certain sets of coprime integers</a>, Proc. Amer. Math. Soc. 16 (1965), 515-521.

%o (PARI) isCC(v)=forprime(p=2,vecmax(v),if(sum(i=1,#v,v[i]%p==0)!=1, return(0)));1

%o A003139(n)=my(v=vector(n-1,i,i+1));sum(i=2^(n-2),2^(n-1)-1, isCC(vecextract(v,i)))

%o a(n)=if(n<3,return(1)); my(p=prime(n));sum(k=precprime(p-1), p-1, A003139(k)) \\ _Charles R Greathouse IV_, Apr 24 2013

%Y Cf. A003139.

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E a(31)-a(44) from _Charlie Neder_, Dec 15 2018

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Last modified September 27 08:50 EDT 2020. Contains 337380 sequences. (Running on oeis4.)